A New Algorithm for Finding Trees with Many Leaves

  • Joachim Kneis
  • Alexander Langer
  • Peter Rossmanith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

Abstract

We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Spanning Out-Tree in the case of directed graphs. The run time of our algorithm is \(O({\it poly}(|V|) + 4^k k^2)\) on undirected graphs, and O(4k |V| ·|E|) on directed graphs. This improves over the previously fastest algorithms for these problems with run times of \(O({\it poly}(|V|) + 6.75^k {\it poly}(k))\) and \(2^{O(k \log k)} {\it poly}(|V|)\), respectively.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Joachim Kneis
    • 1
  • Alexander Langer
    • 1
  • Peter Rossmanith
    • 1
  1. 1.Dept. of Computer ScienceRWTH Aachen UniversityGermany

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